Transcript Significant Figures and Scientific Notation

Significant Figures and
Scientific Notation
Math in the Science Classroom
Scientific Notation
• Scientific notation is the way that scientists
easily handle very large numbers or very
small numbers.
• For example, instead of writing
0.0000000056, we write 5.6 x 10-9. So,
how does this work?
Scientific Notation
10000 = 1 x 104
24327 = 2.4327 x 104
1000 = 1 x 103
7354 = 7.354 x 103
100 = 1 x 102
482 = 4.82 x 102
10 = 1 x 101
89 = 8.9 x 101 (not usually done)
1 = 100
1/10 = 0.1 = 1 x 10-1
0.32 = 3.2 x 10-1 (not usually done)
1/100 = 0.01 = 1 x 10-2
0.053 = 5.3 x 10-2
1/1000 = 0.001 = 1 x 10-3
0.0078 = 7.8 x 10-3
1/10000 = 0.0001 = 1 x 10-4
0.00044 = 4.4 x 10-4
Scientific Notation
• A positive exponent shows that the
decimal point is shifted that number of
places to the right.
• 251 x 104 = 2,510,000
• A negative exponent shows that the
decimal point is shifted that number of
places to the left.
• 251 x 10-4 = .0251
Scientific Notation Practice
1. Write in scientific notation: 0.000467
2. Write in scientific notation 32000000
3. Express 5.43 x 10-3 as a number.
4. Express 6.34 x 109 as a number.
Significant Figures
There are two kinds of numbers in the world:
• exact:
– example: There are exactly 12 eggs in a dozen.
– example: Most people have exactly 10 fingers and 10
toes.
• inexact numbers:
– example: any measurement.
If I quickly measure the width of a piece of notebook
paper, I might get 220 mm (2 significant figures). If I
am more precise, I might get 216 mm (3 significant
figures). An even more precise measurement would
be 215.6 mm (4 significant figures).
PRECISION VS ACCURACY
– Accuracy refers to how closely a measured
value agrees with the correct value.
– Precision refers to how closely individual
measurements agree with each other.
accurate
(the average is
accurate)
not precise
precise
not accurate
accurate
and
precise
Significant Figures
• The number of significant figures is the
number of digits believed to be correct by
the person doing the measuring. It
includes one estimated digit.
• So, does the concept of significant figures
deal with precision or accuracy?
Significant Figures
Consider the beaker pictured below:
•The smallest division is 10 mL, so we can
read the volume to 1/10 of 10 mL or 1 mL.
•We measure 47 mL
•So, How many significant figures does our
volume of 47?
•Answer - 2! The "4" we know for sure
plus the "7" we had to estimate.
Significant Figures
Now consider a graduated cylinder.
• First, note that the surface of the
liquid is curved. This is called the
meniscus.
• The smallest division of this
graduated cylinder is 1 mL.
• We measure 36.5mL
• How many significant figures does
our answer have? 3! The "3" and
the "6" we know for sure and the
"5" we had to estimate a little.
Significant Figures
Rules for Working with Significant Figures:
1. Leading zeros are never significant.
2. Imbedded zeros are always significant.
3. Trailing zeros are significant only if the
decimal point is specified.
Hint: Change the number to scientific
notation. It is easier to see.
Significant Figures
Example
Number of
Significant Figures
Scientific Notation
3
6.82 x 10-3
4
1.072 (x 100)
1
3 x 102
3
3.00 x 102
0.00682
1.072
300
300.
Significant Figures